Bacteriophages follow complex replication dynamics in codependence with their host cells. The corresponding dynamics are usually described with three key parameters: the adsorption rate \(\varphi\) , the burst size \(\beta\) and the latent period \(\tau\) . Single-cell experiments have shown cellular variability in latent period and burst size. Yet, those parameters are traditionally modelled as uniform values for the whole bacterial population, which may introduce bias in the predicted profiles. Here, we systematically assessed the relevance of modelling this cell-level variability in the context of bacteriophage dynamics. We developed a comprehensive modelling framework, aiming to: (i) identify which parameter distributions impact population dynamics, (ii) quantify how difference in distribution can influence predictions, and (iii) inform model selection by comparing relevant modelling approaches. A distributed delay differential equation model with randomly distributed latent period, burst size and adsorption rate within the cell population was developed. It also included logistic growth of the host cell, saturable adsorption rate and intracellular replication dynamics. This model was compared to classical models, both fixed delay differential equation and transit compartments models, over typical ranges of phage parameters. Only the distribution of the latent period and its influence on burst size impacted population dynamics. The two classical models proved to be good approximations of dynamics, but only at low cellular variability. As such, although the classical approaches can be preferred at lower variability, this distributed framework is warranted when high variability is expected, or when the other approaches fail to accurately capture the dynamics.
